Question

Complete the following volume equivalents: (a) \(1 \mathrm{~mL}=? \mathrm{~cm}^{3}\) (b) \(1 \mathrm{in}^{3}=? \mathrm{~cm}^{3}\)

Short answer

(a) 1 mL = 1 cm³; (b) 1 in³ = 16.387064 cm³.

Step-by-step solution

Understanding Milliliters and Cubic Centimeters

A milliliter (mL) is a unit of volume that is commonly used in expressing liquid capacities. A cubic centimeter (cm³) is a unit often used to express volumes of solids. By definition, 1 milliliter is exactly equivalent to 1 cubic centimeter. Thus, \(1 \mathrm{~mL} = 1 \mathrm{~cm}^3\).

Convert Inches to Centimeters for Volume Calculation

To convert a volume from cubic inches to cubic centimeters, first, we need to understand the conversion factor between inches and centimeters. There are 2.54 centimeters in an inch. The formula to convert cubic inches to cubic centimeters is \((1 \text{ inch} = 2.54 \text{ cm})^3\).

Calculate the Conversion Factor from Cubic Inches to Cubic Centimeters

Raise the conversion factor of inches to centimeters to the third power, since it is a cubic measurement: \[\text{Volume from inches to cm}^3 = (2.54\text{ cm/inch})^3 = 16.387064 \text{ cm}^3\]. Thus, \(1 \mathrm{~in}^3 = 16.387064 \mathrm{~cm}^3\).

Key concepts

Cubic Centimeters

A cubic centimeter, often abbreviated as cm³, is a unit used to measure volume. It represents the volume of a cube with sides that are each 1 centimeter long. This means that the entire space within that cube is exactly 1 cm long, 1 cm in height, and 1 cm in width.

Cubic centimeters are widely used in various scientific and medical fields for measuring solid forms. For example:

• Medications frequently use cubic centimeters to ensure precise dosages.
• Everyday objects such as packaging or storage units might use cm³ to express how much they can contain.

In the metric system, cubic centimeters are a convenient way to express smaller volumes, especially when detail is crucial. While larger volumes can use liters or cubic meters, cm³ provides an accurate measurement for smaller items.

Milliliters

A milliliter, symbolized as mL, is primarily a unit utilized for measuring liquids. One milliliter equates to one-thousandth of a liter and is a standard measure in many day-to-day contexts.

Comparatively, the milliliter finds use in various settings:

• In the kitchen for measuring liquid ingredients, like water, milk, or oil.
• In the medical field, milliliters accurately determine liquid medication dosages.

One key point to remember is that 1 milliliter is exactly the same volume as 1 cubic centimeter. This equivalence is widely utilized, making it straightforward to switch between measurements. The understanding of this correlation is vital, particularly when working with formulas or measurements where both terms might interchangeably appear.

Volume Conversion

Volume conversion refers to the process of changing one unit of volume to another. This is crucial when dealing with measurements that require standardization across different unit systems.

To get the hang of volume conversion, it helps to know some basic conversion factors:

• 1 milliliter (mL) is equivalent to 1 cubic centimeter (cm³), allowing for seamless transition between liquid and solid measures.
• When converting inches to centimeters, the conversion factor is 2.54 cm per inch. So, for a volume in cubic inches, this factor should be cubed. This gives us approximately 16.387064 cm³ for every cubic inch (in³).

Understanding these conversions can simplify tasks such as cooking, scientific experiments, or any situation requiring unit adaptations. It emphasizes critical thinking about how volume interacts across different measurement systems, ensuring accuracy and precision in every context.